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Transcript
Resistors in Series and Parallel Circuits Resistors in circuits To determine the current or voltage in a circuit that contains multiple resistors, the total resistance must first be calculated. Resistors parallel. can be combined in series or Resistors in Series When connected in series, the total resistance (Rt) is equal to: Rt = R1 + R2 + R3 +… The total resistance is always larger than any individual resistance. Sample Problem Calculate the total current through the circuit. 15 Ω 10 Ω 6 Ω Rt = 15 Ω +10 Ω + 6 Ω Rt = 31 Ω I = V/Rt = 10 V/ 31 Ω = 0.32 A 10 V Resistors in Series Since charge has only one path to flow through, the current that passes through each resistor is the same. The sum of all potential differences equals the potential difference across the battery. > R value = > V Value 5V 3V 2V 10 V Resistors in Parallel When connected in parallel, the total resistance (Rt) is equal to: 1/Rt = 1/R1 + 1/R2 + 1/R3 +… Due to this reciprocal relationship, the total resistance is always smaller than any individual resistance. Sample Problem Calculate the total resistance through this segment of a circuit. 1/Rt = 1/12 Ω +1/4 Ω + 1/6 Ω 12 Ω 4Ω = 1/12 Ω + 3/12 Ω + 2/12 Ω 1/Rt = 6/12 Ω = ½ Ω Rt = 2 Ω 6Ω Resistors in Parallel Since there is more than one possible path, the current divides itself according to the resistance of each path. smallest resistor = more current passes largest resistor = least current passes Resistors in Parallel The voltage across each resistor in a parallel combination is the same. 10 V 10 V 10 V 10 V Calculate the total resistance in the circuit below 3Ω 2Ω 6Ω 4Ω Rtot = 3 Ω + 2 Ω = 5 Ω Rtot = 6 Ω + 4 Ω = 10 Ω Rtot = 3 1/3 Ω + - 1/Rtot = 2/10 Ω+ 1/10 Ω = 3/10 Ω